Question

A right △ABC is inscribed in circle k(O, r). Find the radius of this circle if:

m∠C = 90°, AC = 18 cm, m∠B = 30°.


Thank you!

Answer 1

We have been given that a right △ABC is inscribed in circle k(O, r).

m∠C = 90°, AC = 18 cm, m∠B = 30°. We are asked to find the radius of the circle.

First of all, we will draw a diagram that represent the given scenario.

We can see from the attached file that AB is diameter of circle O and it a hypotenuse of triangle ABC.

We will use sine to find side AB.

`\text{sin}=\frac{\text{Opposite}}{\text{Hypotenuse}}`

`\text{sin}(30^(\circ))=(AC)/(AB)`

`\text{sin}(30^(\circ))=(18)/(AB)`

`AB=\frac{18}{\text{sin}(30^(\circ))}`

`AB=(18)/(0.5)`

`AB=36`

Wee know that radius is half the diameter, so radius of given circle would be half of the 36 that is
`(36)/(2)=18`.

Therefore, the radius of given circle would be 18 cm.